Given any two \(2m_k\times 2m_k\)  matrices of square block form
\(M_k = ({\begin{matrix}A_k & B_k\\ C_k & D_k\end{matrix}} )\)  with \(k=1, 2\) ,
the symplectic sum of \(M_1\)  and \(M_2\)  is defined (cf. [1]}) by
the following \(2(m_1+m_2)\times 2(m_1+m_2)\)  matrix \(M_1{\rm \diamond }M_2\) :
\(M_1{\rm \diamond }M_2=\begin{pmatrix}A_1 & 0 & B_1 & 0\\0 & A_2 & 0 & B_2\\C_1 & 0 & D_1 & 0\\0 & C_2 & 0 & D_2\end{pmatrix}.\) 
